4.7 Article

Dimension Estimation in Noisy PCA With SURE and Random Matrix Theory

Journal

IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 56, Issue 12, Pages 5804-5816

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2008.2005865

Keywords

Model order selection; principal component analysis (PCA); random matrix theory; Stein's unbiased risk estimator (SURE)

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Principal component analysis (PCA) is one of the best known methods for dimensionality reduction. Perhaps the most important problem in using PCA is to determine the number of principal components (PCs) or equivalently choose the rank of the loading matrix. Many methods have been proposed to deal with this problem but almost all of them fail in the important practical case when the number of observation is comparable to the number of variables, i.e., the realm of random matrix theory (RMT). In this paper we propose to use Stein's unbiased risk estimator (SURE) to estimate, with some assistance from RMT, the number of principal components. The method is applied both on simulated and real functional magnetic resonance imaging (fMRI) data, and compared to BIC and the Laplace method.

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